No Feature Movement
A preliminary question, explicitly addressed in Chomsky 1995, is why the complex operation described above as movement (Agree þ Internal Merge) cannot simply occur at the level of features, and some kind of (generalized) pied-piping is necessarily involved—in other words, why features cannot move. Chomsky’s first tentative answer is that features cannot move owing to a phonological constraint:
For the most part—perhaps completely—it is properties of the phonological com ponent that require such pied-piping. Isolated features and other scattered parts of words may not be subject to its rules. (Chomsky 1995, 262–263)
The problem with this proposal is that it implies that post-Spell-Out movement, being free from any phonological constraint, should display no pied-piping. There is good evidence, however, of the existence of pied-piping—that is, of phrasal movement—at LF.
A simple case providing evidence for covert phrasal movement is antecedent-contained deletion: in (1), where the deleted VP is contained within its antecedent, the only way to recover ellipsis without descending into infinite regress is to allow quantifier raising of the phrase every city Bill does.

A more convincing alternative is to identify the constraint banning feature movement with a property of Merge. When it applies to the numeration, Merge indeed is restricted to operate on lexical items, on bundles of features. It is thus natural and minimal to assume that this restriction holds as well when Merge is part of a movement operation. Let us then assume that there is a single operation Merge in the syntax, which applies freely and is constrained to operate on words (Matushansky 2006).
Assuming that features cannot move (or better, be merged), some sort of pied-piping is required. The minimal amount of material a feature should pied-pipe to form a mergeable object is a word, that is, a head. This derives head movement. What about XP-movement? Being anti minimal, why should it exist at all?